Skip to main content
SpringerLink
Log in

Stability improvement of a dynamic walking system via reversible switching surfaces

  • Published:
Multibody System Dynamics Aims and scope Submit manuscript

Abstract

Inspired by the effects of a switching surface on the stability of passive dynamic walking (Safa and Naraghi in Robotica 33(01):195–207, 2015; Safa et al. in Nonlinear Dyn. 81(4):2127–2140, 2015), this paper suggests a new control strategy for stabilization of dynamic bipedal locomotion. It verifies that the stability improvement of a dynamic walking system is feasible while preserving the speed, step-length, period, natural dynamics, and the energy effectiveness of the gait. The proposed control policy goes behind the three primary principles: (i) The system’s switching surface has to be replaced by a new one if an external disturbance is induced. (ii) The new switching surface has to be reshaped back into its old style, together with the disturbance rejection. (iii) The stabilization procedure has to be performed with as small energy consumption as possible. Because of the reversibility effects of the switching surfaces in the above rules, the terminology of “Reversible Switching Surfaces” (RSS) is employed to address the control scheme; so the control objective would be the implementation of RSS for a bipedal robotic system. In this paper, this aim is achieved by a kinematically controlled foot scheme that is implemented on a simple structured biped. The presented idea is validated by a commercial version of MSC Adams software.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  1. http://www.bostondynamics.com

  2. Ames, A.D., Galloway, K., Sreenath, K., Grizzle, J.W.: Rapidly exponentially stabilizing control Lyapunov functions and hybrid zero dynamics. IEEE Trans. Autom. Control 59(4), 876–891 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bhounsule, P.: A controller design framework for bipedal robots: trajectory optimization and event-based stabilization. PhD thesis, Cornell University (2012)

  4. Bhounsule, P.A.: Control of a compass gait walker based on energy regulation using ankle push-off and foot placement. Robotica 33(06), 1314–1324 (2015)

    Article  Google Scholar 

  5. Bhounsule, P.A., Cortell, J., Grewal, A., Hendriksen, B., Karssen, J.D., Paul, C., Ruina, A.: Low-bandwidth reflex-based control for lower power walking: 65 km on a single battery charge. Int. J. Robot. Res. 33(10), 1305–1321 (2014)

    Article  Google Scholar 

  6. Collins, S., Ruina, A., Tedrake, R., Wisse, M.: Efficient bipedal robots based on passive-dynamic walkers. Science 307(5712), 1082–1085 (2005)

    Article  Google Scholar 

  7. Consolini, L., Maggiore, M.: Control of a bicycle using virtual holonomic constraints. Automatica 49(9), 2831–2839 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  8. Freidovich, L., Robertsson, A., Shiriaev, A., Johansson, R.: Periodic motions of the pendubot via virtual holonomic constraints: theory and experiments. Automatica 44(3), 785–791 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  9. Garcia, M., Chatterjee, A., Ruina, A., Coleman, M.: The simplest walking model: stability, complexity, and scaling. J. Biomech. Eng. 120(2), 281–288 (1998)

    Article  Google Scholar 

  10. Giesbers, J.: Contact mechanics in MSC ADAMS—a technical evaluation of the contact models in multibody dynamics software MSC ADAMS. BSc thesis, University of Twente (2012)

  11. Goswami, A., Thuilot, B., Espiau, B.: A study of the passive gait of a compass-like biped robot symmetry and chaos. Int. J. Robot. Res. 17(12), 1282–1301 (1998)

    Article  Google Scholar 

  12. Grizzle, J.W., Abba, G., Plestan, F.: Asymptotically stable walking for biped robots: analysis via systems with impulse effects. IEEE Trans. Autom. Control 46(1), 51–64 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  13. Hamed, K.A., Grizzle, J.W.: Robust event-based stabilization of periodic orbits for hybrid systems: application to an underactuated 3d bipedal robot. In: 2013 American Control Conference, pp. 6206–6212. IEEE Press, New York (2013)

    Chapter  Google Scholar 

  14. Hamed, K.A., Grizzle, J.W.: Event-based stabilization of periodic orbits for underactuated 3-d bipedal robots with left-right symmetry. IEEE Trans. Robot. 30(2), 365–381 (2014)

    Article  Google Scholar 

  15. Hamed, K.A., Grizzle, J.W.: Iterative robust stabilization algorithm for periodic orbits of hybrid dynamical systems: application to bipedal running. IFAC-PapersOnLine 48(27), 161–168 (2015)

    Article  Google Scholar 

  16. Hasaneini, S.J., Macnab, C.J., Bertram, J.E., Leung, H., et al.: Optimal relative timing of stance push-off and swing leg retraction. In: IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 3616–3623 (2013)

    Chapter  Google Scholar 

  17. Hobbelen, D.G.: Limit cycle walking (2008)

  18. Hürmüzlü, Y., Moskowitz, G.D.: The role of impact in the stability of bipedal locomotion. Dyn. Stab. Syst. 1(3), 217–234 (1986)

    MATH  Google Scholar 

  19. Hürmüzlü, Y., Moskowitz, G.D.: Bipedal locomotion stabilized by impact and switching: I. Two-and three-dimensional, three-element models. Dyn. Stab. Syst. 2(2), 73–96 (1987)

    MATH  Google Scholar 

  20. Hürmüzlü, Y., Moskowitz, G.D.: Bipedal locomotion stabilized by impact and switching: II. Structural stability analysis of a four-element bipedal locomotion model. Dyn. Stab. Syst. 2(2), 97–112 (1987)

    MATH  Google Scholar 

  21. Iqbal, S., Zang, X., Zhu, Y., Zhao, J.: Bifurcations and chaos in passive dynamic walking: a review. Robot. Auton. Syst. 62(6), 889–909 (2014)

    Article  Google Scholar 

  22. Kuo, A.D.: Energetics of actively powered locomotion using the simplest walking model. J. Biomech. Eng. 124(1), 113–120 (2002)

    Article  Google Scholar 

  23. Maggiore, M., Consolini, L.: Virtual holonomic constraints for Euler–Lagrange systems. IEEE Trans. Autom. Control 58(4), 1001–1008 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  24. McGeer, T.: Passive dynamic walking. Int. J. Robot. Res. 9(2), 62–82 (1990)

    Article  Google Scholar 

  25. Montanari, M., Ronchi, F., Rossi, C., Tonielli, A.: Control of a camless engine electromechanical actuator: position reconstruction and dynamic performance analysis. IEEE Trans. Ind. Electron. 51(2), 299–311 (2004)

    Article  Google Scholar 

  26. Raibert, M., Blankespoor, K., Nelson, G., Playter, R.: Bigdog, the rough-terrain quadruped robot. IFAC Proc. Vol. 41(2), 10,822–10,825 (2008)

    Article  Google Scholar 

  27. Raibert, M.H.: Legged Robots that Balance. MIT Press, Cambridge (1986)

    Book  MATH  Google Scholar 

  28. Ramezani, A., Hurst, J.W., Hamed, K.A., Grizzle, J.: Performance analysis and feedback control of ATRIAS, a three-dimensional bipedal robot. J. Dyn. Syst. Meas. Control 136(2), 1–12 (2014)

    Article  Google Scholar 

  29. Rezazadeh, S., Hubicki, C., Jones, M., Peekema, A., Van Why, J., Abate, A., Hurst, J.: Spring-mass walking with ATRIAS in 3D: robust gait control spanning zero to 4.3 kph on a heavily underactuated bipedal robot. In: ASME 2015 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, New York (2015)

    Google Scholar 

  30. Safa, A., Naraghi, M., Aalasty, A.: Application of local slopes in the study of metastable walking. In: Assistive Robotics: 18th International Conference on Climbing and Walking Robots (CLAWAR), pp. 337–344. World Scientific, Singapore (2015)

    Chapter  Google Scholar 

  31. Safa, A.T., Alasty, A., Naraghi, M.: A different switching surface stabilizing an existing unstable periodic gait: an analysis based on perturbation theory. Nonlinear Dyn. 81(4), 2127–2140 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  32. Safa, A.T., Mohammadi, S., Hajmiri, S.E., Naraghi, M., Alasty, A.: How local slopes stabilize passive bipedal locomotion? Mech. Mach. Theory 100, 63–82 (2016)

    Article  Google Scholar 

  33. Safa, A.T., Naraghi, M.: The role of walking surface in enhancing the stability of the simplest passive dynamic biped. Robotica 33(01), 195–207 (2015)

    Article  Google Scholar 

  34. Safa, A.T., Naraghi, M., Alasty, A.: Optimization of the switching surface for the simplest passive dynamic biped. In: International Conference on Advanced Robotics (ICAR), pp. 363–368 (2015)

    Google Scholar 

  35. Sakagami, Y., Watanabe, R., Aoyama, C., Matsunaga, S., Higaki, N., Fujimura, K.: The intelligent ASIMO: system overview and integration. In: IEEE/RSJ International Conference on Intelligent Robots and Systems, vol. 3, pp. 2478–2483 (2002)

    Chapter  Google Scholar 

  36. Shiriaev, A.S., Freidovich, L.B., Robertsson, A., Johansson, R., Sandberg, A.: Virtual-holonomic-constraints-based design of stable oscillations of furuta pendulum: theory and experiments. IEEE Trans. Robot. 23(4), 827–832 (2007)

    Article  Google Scholar 

  37. Sreenath, K., Park, H.W., Poulakakis, I., Grizzle, J.W.: A compliant hybrid zero dynamics controller for stable, efficient and fast bipedal walking on MABEL. Int. J. Robot. Res. 30(9), 1170–1193 (2011)

    Article  Google Scholar 

  38. Vukobratović, M., Borovac, B.: Zero-moment point—thirty five years of its life. Int. J. Humanoid Robot. 1(01), 157–173 (2004)

    Article  Google Scholar 

  39. Vukobratović, M., Juricic, D.: Contribution to the synthesis of biped gait. IEEE Trans. Biomed. Eng. 1, 1–6 (1969)

    Article  Google Scholar 

  40. Westervelt, E., Morris, B., Farrell, K.: Analysis results and tools for the control of planar bipedal gaits using hybrid zero dynamics. Auton. Robots 23(2), 131–145 (2007)

    Article  Google Scholar 

  41. Westervelt, E.R., Grizzle, J.W., Koditschek, D.E.: Hybrid zero dynamics of planar biped walkers. IEEE Trans. Autom. Control 48(1), 42–56 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  42. Ylikorpi, T., Peralta, J.L., Halme, A.: Comparing passive walker simulators in Matlab and Adams. J. Struct. Mech. 44(1), 65–92 (2011)

    Google Scholar 

Download references

Acknowledgements

The first and last authors are grateful to Iran National Science Foundation (INSF) for partially supporting the research.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Amirkabir University of Technology, Tehran, 15875, Iran

    Ali Tehrani Safa, Somaye Mohammadi & Mahyar Naraghi

  2. Department of Mechanical Engineering, Sharif University of Technology, Tehran, 14588, Iran

    Aria Alasty

Authors
  1. Ali Tehrani Safa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Somaye Mohammadi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mahyar Naraghi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Aria Alasty
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ali Tehrani Safa.

Electronic Supplementary Material

Below is the link to the electronic supplementary material.

(MP4 6.7 MB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Safa, A.T., Mohammadi, S., Naraghi, M. et al. Stability improvement of a dynamic walking system via reversible switching surfaces. Multibody Syst Dyn 43, 349–367 (2018). https://doi.org/10.1007/s11044-017-9593-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11044-017-9593-4

Keywords

Search

Navigation